Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been as-cribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we createin silicoglasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than kBTQ, with TQ the temperature below which quantum effects are relevant (TQ≈1 K in most experiments). We find thatas the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore thereal-space nature of tunneling defects, and find that they are mostly localized to a few atoms, butare occasionally dramatically delocalized